Symmetries of certain physical theories and the Jordan algebras

Journal Article · Sat Jun 20 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92001617· OSTI ID:7035918

Foot, R; Joshi, G C ^[1]

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1. School of Physics, Univ. of Melbourne, Parkville, Victoria, 3052 (AU)

In this paper, it is shown that the sequence of Jordan algebras M{sup n}{sub 3}, whose elements are the 3 {times} 3 Hermitian matrices over the division algebras R, C, Q and O, can be associated with the bosonic string as well as the superstring. The construction reveals that the space-time symmetries of the first-quantized bosonic string and superstring actions can e related. The bosonic string and the superstring are associated with the exceptional Jordan algebra while the other Jordan algebras in the M{sup n}{sub 3} sequence can be related to parastring theories. We then proceed to further investigate a connection between the symmetries of supersymmetric Lagrangians and the transformations associated with the structure group of M{sup n}{sub 3}. The N = 1 on-shell supersymmetric Lagrangians in 3, 4 and 6 dimensions with a spin 0 field and a spin 1/2 field re incorporated within the Jordan-algebraic framework. The authors also make some remarks concerning a possible role for the division algebras in the construction of higher-dimensional extended objects.

• OSTI ID: 7035918
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:15; ISSN 0217-751X; ISSN IMPAE
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
CLASSIFICATION
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FUNCTIONS
HERMITIAN OPERATORS
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
PARTICLE MODELS
QUANTIZATION
QUARK MODEL
SPACE-TIME
STRING MODELS
SUPERSTRING MODELS
SYMMETRY
TRANSFORMATIONS